Hand-to-hand combat with multi-thousand-digit integrals.

Bailey, D.H. and Borwein, Jonathan M. (2012) Hand-to-hand combat with multi-thousand-digit integrals. Journal of Computational Science, 3 . pp. 77-86.

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    In this paper we describe numerical investigations of definite integrals that arise by considering the moments of multi-step uniform random walks in the plane, together with a closely related class of integrals involving the elliptic functions K, K',E and E'. We find that in many cases such integrals can be “experimentally” evaluated in closed form or that intriguing linear relations exist within a class of similar integrals. Discovering these identities and relations often requires the evaluation of integrals to extreme precision, combined with large-scale runs of the “PSLQ” integer relation algorithm. This paper presents details of the techniques used in these calculations and mentions some of the many difficulties that can arise.

    Item Type: Article
    Subjects: UNSPECIFIED
    Faculty: UNSPECIFIED
    Depositing User: Dr David Allingham
    Date Deposited: 05 Oct 2012 13:13
    Last Modified: 03 Jan 2015 21:21

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